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Journal of the Optical Society of America B

Generation of a focused hollow beam by an 2pi-phase plate and its application in atom or molecule optics

Yong Xia, Jianping Yin

Published Mar 1, 2005• 30 citations
Publisher

Abstract

We propose a new scheme to generate a focusing hollow beam (FHB) by use of an azimuthally distributed 2pi-phase plate and a convergent thin lens. From the Fresnel diffraction theory, we calculate the intensity distributions of the FHB in free propagation space and study the relationship between the waist w_0 of the incident Gaussian beam (or the focal length f of the lens) and the dark spot size (or the beam radius) at the focal point and the relationship between the maximum radial intensity of the FHB and the dark spot size (or the beam radius) at the focal point, respectively. Our study shows that the FHB can be used to cool and trap neutral atoms by intensity-gradient-induced Sisyphus cooling due to an extremely high intensity gradient of the FHB itself near the focal point, or to guide and focus a cold molecular beam. We also calculate the optical potential of the blue-detuned FHB for ^85Rb atoms and find that in the focal plane, the smaller the dark spot size of the FHB is, the higher the optical potential is, and the greater the corresponding optimal detuning delta is; these qualities are beneficial to an atomic lens not only because it is profitable to obtain an atomic lens with a higher resolution, but also because it is helpful to reduce the spontaneous photon-scattering effect of atoms in the FHB.

DOI
10.1364/josab.22.000529

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Acta Physica Sinica•Jan 1, 2016•3 citations
We propose a new scheme to generate a focusing hollow beam (FHB) by use of an azimuthally distributed 2pi-phase plate and a convergent thin lens. From the Fresnel diffraction theory, we calculate the intensity distributions of the FHB in free propagation space and study the relationship between the waist w_0 of the incident Gaussian beam (or the focal length f of the lens) and the dark spot size (or the beam radius) at the focal point and the relationship between the maximum radial intensity of the FHB and the dark spot size (or the beam radius) at the focal point, respectively. Our study shows that the FHB can be used to cool and trap neutral atoms by intensity-gradient-induced Sisyphus cooling due to an extremely high intensity gradient of the FHB itself near the focal point, or to guide and focus a cold molecular beam. We also calculate the optical potential of the blue-detuned FHB for ^85Rb atoms and find that in the focal plane, the smaller the dark spot size of the FHB is, the higher the optical potential is, and the greater the corresponding optimal detuning delta is; these qualities are beneficial to an atomic lens not only because it is profitable to obtain an atomic lens with a higher resolution, but also because it is helpful to reduce the spontaneous photon-scattering effect of atoms in the FHB.
We propose a new method to generate a focused hollow laser beam by using an azimuthally distributed 2π-phase plate and a convergent thin lens,and calculate the intensity distribution of the focused hollow beam in free propagation space.The relationship between the waist w0 of the incident collimated Gaussian beam and the dark spot size of the focused hollow beam at the focal point,and the relationship between the focal lenght f of the thin lens and the dark spot size are studied respectively.The optical potential of the blue-detuned focused hollow beam for^85 Rb atoms is calculated.Our study shows that when the larger waist w of the incident Gaussian beam and the shorter focal length f of the lens are chosen,we can obtain an extremely small dark spot size of the focused hollow beam,which can be used to form an atomic lens with a resolution of sereval angstroms.
We propose a new method to generate a focused hollow laser beam by using an azimuthally distributed 2π-phase plate and a convergent thin lens, and calculate the intensity distribution of the focused hollow beam in free propagation space. The relationship between the waist w o of the incident collimated Gaussian beam and the dark spot size of the focused hollow beam at the focal point, and the relationship between the focal length f of the thin lens and the dark spot size are studied respectively. The optical potential of the blue-detuned focused hollow beam for 85 Rb atoms is calculated. Our study shows that when the larger waist w of the incident Gaussian beam and the shorter focal length f of the lens are chosen, we can obtain an extremely small dark spot size of the focused hollow beam, which can be used to form an atomic lens with a resolution of several angstroms.
We report the generation of a crossed, focused, optical vortex beam by using a pair of hybrid holograms, which combine the vortex phase and lens phase onto a spatial light modulator. We study the intensity distributions of the vortex beam in free propagation space, and the relationship of its dark spot size with the incident Gaussian beam’s waist, the lens’s focal length, and its orbital angular momentum. Our results show that the crossed, focused, vortex beam’s dark spot size can be as small as 16.3 μm and adjustable by the quantum number of the orbital angular momentum, and can be used to increase the density of trapped molecules. Furthermore, we calculate the optical potential of the blue-detuned, crossed vortex beam for MgF molecules. It is applicable to cool and trap neutral molecules by intensity-gradient-induced Sisyphus cooling, as the intensity gradient of such vortex beam is extremely high near the focal point.
Abstract A succinct experimental scheme is demonstrated to generate a localized hollow beam by using a π -phase binary bitmap and a convergent thin lens. The experimental results show that the aspect ratio of the dark-spot size of the hollow beam can be effectively controlled by the focal length of the lens. The measured beam profiles in free space also agree with the theoretical modeling. The studies hold great promise that such a hollow beam can be used to cool trapped atoms (or molecules) by Sisyphus cooling and to achieve an optically-trapped Bose–Einstein condensate by optical-potential evaporative cooling.
In this paper, we propose a new scheme to generate a dark hollow-beam, which includes dark hollow-beam optical pipe and hollow-beam optical dipole trap, through using a system composed of a four steps phase plate and a spherical lens. This kind of light beam can be used to focus, guide and trap the cold atom. We also calculate the intensity distributing and characteristic parameters of a dark hollow-beam and the optical dipole potential which manipulate the cold atoms of 85Rb. At last, we analyze and demonstrate the experimental feasibility of the scheme.
In order to generate a submicron localized hollow laser beam and realize the more efficient laser cooling and trapping of a single atom, a simple and promising scheme with using the system of a single mode fiber a circle binary phase plate and a microlens is proposed in this paper. From Rayleigh-Sommerfeld diffraction theory, the intensity distribution of the generated localized hollow laser beam near the focal plane and its propagating properties in free space are calculated. Also, the dependences of the dark-spot size of the localized hollow beam on the mode radius of single mode fiber and the focal length of the mocrolens are studied. The calculated results show that the intensity distribution of the localized hollow beam presents approximately symmstrical distribution near the focal plane. In the center of the focal plane, the light intensity is 0 and increases gradually around it. So a closed spherical light field (i.e., localized hollow laser beam) with a radius of 0.4 m is generated. The calculated results also show that the dark-spot size of the localized hollow laser beam decreases with the increasing of the microlens focal length and the decreasing of the single mode fiber mode radius. So proper parameters of this optical system can be chosen to generate localized hollow laser beams with different sizes for various applications. When the localized hollow laser beam is blue detuned, atoms will be trapped in the minimum light filed. If a repumping laser beam is applied, the trapped atoms will be also cooled by the intensity-gradient Sisyphus cooling. In this paper, we build a device for trapping and cooling a single atom by using the generated blue detuned submicron localized hollow laser beam. We study the dynamical process of intensity-gradient cooling of a single 87Rb atom trapped in the localized hollow beam by Monte-Carlo method. Our study shows that a single 87Rb atom with a temperature of 120 K (the corresponding momentum is 30ħk) from a magneto-optical trap (MOT) can be directly cooled to a final tempreture of ～ 5.8 K (the corresponding momentum is ～ 6.6ħk). So an ultracold single atom is generated and trapped in our submicro localized hollow beam. This device for obtaining ultralcold single atom can be widely uesd in the regions of the optical physics, the atom and molecule optics, such as the detecting of the fundamental physical parameters, realizing the quantum computer, studying the cold collision of singe atoms, and realizing the single atom laser.